时间分割法正弦曲线插补算法研究

An Approach to the Time Slicing Interpolation Algorithm for a Sine Curve

根据时间分割法的基本思想，从正弦曲线运动的物理意义出发，推导出插补正弦曲线的数学模型，提出一种新算法，分析了理论插补精度，编制出相应的轨迹插补程序，这种插补方法可获得较高的插补精度和插补速度，适用于不带数学协处理器的数控系统。

The interpolation algorithm for a sine curve based on the principle of the tiem-slicingmethod and the physical meaning of sinusoidal motion is proposed.A sine curve can be ap-proximated by chords of equal length and each chord is to be machined within a time intervalof the same period. By mapping a sinusoidal motion onto its reference circle,the feed incre-ments along the active axis can be calculated with an iterative formula while that along thepassive axis can be obtained with a recursive formula based on the method of angular approx-imatiOn on the reference circle. With this algorithm,a position error smaller than the trunca-tion error can be guaranteed.An analysis of the approximation accuracy has led to the rela-tionship between it and the feedrate and the corresponding formula for feedrate selection.The correctness of this algorithm has been proved by simulation and industrial tests.